differential (calculus)

In mathematics, differential calculus is about the way a function changes, in particular the (first) differential of a simple function of one variable is its slope. For a simple (single variable) function this is a single number representing the rate of growth (or decline) of the function. For a function of more than one variable, say the height of terrain on a map, the (first) differential is a vector representing the size and direction of maximum ascent. The second differential is the rate of change of the first differential; for example, velocity is the rate of change of location (first differential) and accelaration is the rate of change of velocity (second differential). Higher differentials are used also, for example, in planning train lines engineers consider 'jerk', the rate of change of acceleration, which is a third differential.